First, STP is not able to do multi-track recordings, it's limited to one mono or stereo track. You'll need another software to do that. Garage Band can do that (maximum 8 inputs) or if you want a more professional solution, there's Digital Performer or Logic.
Most professional mixing boards have a direct out on mic inputs. Usually, this feed is post-preamp, pre-EQ. You simply need to take those outs and input them in an audio interface. I often use a MOTU 828mkII for this and it works very well. Also, if you buy a 828, it comes with AudioDesk, an audio-only version of Digital Performer.